Do my prayers and ablution (wudu') become invalid if I step with a wet foot or wet clothing on a spot I thought was ritually impure (najis), and I prayed with that ablution and clothing, then it later became clear to me that it was indeed impure, or there was a possibility of its impurity?

Ignore the [waswas] (whispers of Satan) and do not rule a place impure unless you have absolute certainty. The default state is purity. For anything you are certain is impure, it is sufficient to purify it by pouring water over it until it is submerged. Your prayers are valid, and it is not permissible to pray in a place you know to be impure before purifying it.